Do Not Disturb does not have the caller hear a busy signal. The call just goes to Voicemail. Do Not Disturb silences the notifications you receive, it does not decline the call.
If you use Mute, as the other caller recommends, you should only get a vibration if turned on during the night to disturb you and make you look at the phone, unless you are referring to the screen lighting up. Do Not Disturb is what you would need to use if you wish to not hear any notifications. If your callers decide to call back immediately after going to voicemail, then you need to turn off the Repeated Calls switch, so the calls cannot get through. The same with setting your Allow Calls From. If you do not wish to be disturbed at all by anyone, then set that to No One.